Finite Group Databasebeta

← #15777062

Subgroups — #15777062

Order 3328.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13116984C211yesmaximal, characteristic
2#13116878C211yesmaximal, characteristic
3#13114430C211yesmaximal, characteristic, complemented
4#13113630C211yesmaximal, characteristic
5#13112899C211yesmaximal, characteristic, complemented
6#13112895C211yesmaximal, characteristic, complemented
7C13×#1362C211yesmaximal, characteristic, complemented
8C13×#494C2211yescharacteristic
9C2×#88068—21no—
10#11718754—21no—
11#11718740—21no—
12#11718495—21no—
13C4×D104C2211yescharacteristic
14#11718343C2211yescharacteristic
15C13×C4⋊C16C2211yescharacteristic
16C13×#335C2211yescharacteristic
17#11718156—21no—
18#11718101—21no—
19#11718097—21no—
20#11718075—21no—
21C4⋊#6090C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C13×C4⋊Q8—21no—
26C2×D104D411yescharacteristic
27C2×C8×D13—41no—
28C4×D52—21no—
29#88123—21no—
30C2×C13×C16—21no—
31C13×C4⋊C8—21no—
32C4×C8×C13C2311yescharacteristic
33#88068—42no—
34#88061—21no—
35#88060—41no—
36#88058—21no—
37#88058—21no—
38#88058D411yescharacteristic
39C2×#6090—21no—
40#88050—42no—
41#88048—41no—
42#88048—41no—
43C4×#1055D411yescharacteristic
44C4×#1055D411yescharacteristic
45#12420—131nomaximal, Sylow
46C2×Q8×C13—41no—
47C2×D52—21no—
48C2×C4×D13—41no—
49C2×Dic26—41no—
50C13×Q16—41no—
51C13×Q16—41no—
52C13×Q16—81no—
53C2×C8×C13—41no—
54C2×C8×C13C2×D411yescharacteristic
55C2×C8×C13#4111yescharacteristic
56C13×C4⋊C4—41no—
57C13×C4⋊C4—41no—
58C42×C13C2×D411yescharacteristic
59#6103—41no—
60C4⋊Dic13—21no—
61C4⋊Dic13—41no—
62C4⋊Dic13—41no—
63C2×#1055—21no—
64C2×#1055D811yescharacteristic
65C2×#1055D811yescharacteristic
66D104—21no—
67D104SD1612yes—
68C8×D13—82no—
69C13×C16—41no—
70#6090—41no—
71#2226—131no—
72#2208—131no—
73#1707—131no—
74C8×D8—131no—
75#1367—131no—
76#1365—131no—
77#1362D1311yescharacteristic, complemented
78C22×D13—41no—
79Q8×C13—81no—
80Q8×C13—81no—
81C2×C4×C13—81no—
82C2×C4×C13#12111yescharacteristic
83C2×C4×C13C2×D811yescharacteristic
84C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
85C2×Dic13—41no—
86C2×Dic13—81no—
87D52—22no—
88D52—41no—
89C4×D13—81no—
90C4×D13—81no—
91Dic26—82no—
92C8×C13—21no—
93C8×C13—81no—
94C8×C13C2×SD1611yescharacteristic
95C8×C13#13511yescharacteristic
96#1055—21no—
97#1055—41no—
98#1055SD3212yescomplemented
99C2×SD32—261no—
100#500—131no—
101#498—261no—
102#494C2×D1311yescharacteristic
103#487—261no—
104C4×D8—131no—
105C8×D4—261no—
106#367—261no—
107C4⋊C16—131no—
108C4⋊C16C2×D1311yescharacteristic
109#358—261no—
110#357—261no—
111#335C2×D1311yescharacteristic
112D4⋊C8—261no—
113C82—131no—
114C22×C13#45911yescharacteristic
115C2×D13—42no—
116C2×D13—81no—
117C2×D13—81no—
118C4×C13—21no—
119C4×C13—161no—
120C4×C13#46511yescharacteristic
121C4×C13#47111yescharacteristic
122C4×C13C2×SD3211yescharacteristic
123C4×C13#51011yescharacteristic
124Dic13—81no—
125Dic13—161no—
126C2×Q16—21no—
127C2×Q16—21no—
128C2×D8—131no—
129C22×C8—521no—
130C4⋊Q8—21no—
131C4⋊Q8—261no—
132C4×D4—261no—
133SD32—522no—
134C2×C16—21no—
135C2×C16—261no—
136#107—131no—
137#107—261no—
138#107—261no—
139#106—521no—
140#106—521no—
141C4⋊C8—21no—
142#103—522no—
143#102—261no—
144C22⋊C8—521no—
145C4×C8—131no—
146C4×C8—131no—
147C4×C8C22×D1311yescharacteristic
148C2×C13#166511yescharacteristic
149C2×C13#220811yescharacteristic
150C2×C13#221211yescharacteristic
151D13—82no—
152C2×Q8—41no—
153C2×Q8—521no—
154C2×D4—261no—
155C22×C4—521no—
156Q16—41no—
157Q16—41no—
158Q16—81no—
159D8—132no—
160D8—261no—
161C2×C8—41no—
162C2×C8—131no—
163C2×C8—131no—
164C2×C8—261no—
165C2×C8—1042no—
166C2×C8#612711yescharacteristic
167C2×C8D4×D1311yescharacteristic
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—261no—
171C4⋊C4—521no—
172C4⋊C4—521no—
173C22⋊C4—521no—
174C42D4×D1311yescharacteristic
175C16—41no—
176C16—521no—
177C13#1242011yescharacteristic, complemented, Sylow
178C23—521no—
179Q8—81no—
180Q8—81no—
181Q8—1042no—
182D4—262no—
183D4—521no—
184C2×C4—81no—
185C2×C4—521no—
186C2×C4—1041no—
187C2×C4—1041no—
188C2×C4—1041no—
189C2×C4#8813811yescharacteristic
190C2×C4D8×D1311yescharacteristic
191C2×C4#8816811yescharacteristic
192C8—21no—
193C8—81no—
194C8—132no—
195C8—261no—
196C8—521no—
197C8#8816611yescharacteristic
198C8SD16×D1311yescharacteristic
199C22—522no—
200C22—1041no—
201C22—1041no—
202C22#1171844711yescharacteristic
203C4—21no—
204C4—161no—
205C4—1041no—
206C4—2081no—
207C4#1171840911yescharacteristic
208C4#1171843911yescharacteristic
209C4D13×SD3211yescharacteristic
210C4#1171857911yescharacteristic
211C2—1042no—
212C2#1311417611yescharacteristic
213C2#1311688011yescharacteristic
214C2#1311690811yescharacteristic
subgroupG/H
centerC22#11718447
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1362C2
socleC22×C13#459
prime radicalC2×D104D4
hypercenter#1362D13
hypocenterC13#12420
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #13114430C2semidirect
5. #13112899C2semidirect
6. #13112895C2semidirect
7. C13×#1362C2semidirect
77. #1362D13semidirect
98. #1055SD32semidirect
177. C13#12420semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131169842
#131168782
#131144302
#131136302
#131128992
#131128952
C13×#13622
#1242013